Abstract
Much work has been done on the computation of market equilibria. However due to strategic play by buyers, it is not clear whether these are actually observed in the market. Motivated by the observation that a buyer may derive a better payoff by feigning a different utility function and thereby manipulating the Fisher market equilibrium, we formulate the Fisher market game in which buyers strategize by posing different utility functions. We show that existence of a conflict-free allocation is a necessary condition for the Nash equilibria (NE) and also sufficient for the symmetric NE in this game. There are many NE with very different payoffs, and the Fisher equilibrium payoff is captured at a symmetric NE. We provide a complete polyhedral characterization of all the NE for the two-buyer market game. Surprisingly, all the NE of this game turn out to be symmetric and the corresponding payoffs constitute a piecewise linear concave curve. We also study the correlated equilibria of this game and show that third-party mediation does not help to achieve a better payoff than NE payoffs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adsul, B., Babu, C.S., Garg, J., Mehta, R., Sohoni, M.: Nash equilibria in Fisher market. arXiv:1002.4832 (2010)
Amir, R., Sahi, S., Shubik, M., Yao, S.: A strategic market game with complete markets. Journal of Economic Theory 51, 126–143 (1990)
Brainard, W.C., Scarf, H.E.: How to compute equilibrium prices in 1891. Cowles Foundation, Discussion Paper-1272 (2000)
Bu, T., Deng, X., Qi, Q.: Forward looking Nash equilibrium for keyword auction. Inf. Process. Lett. 105(2), 41–46 (2008)
Chakrabarty, D., Devanur, N.R., Vazirani, V.V.: New results on rationality and strongly polynomial solvability in Eisenberg-Gale markets. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 239–250. Springer, Heidelberg (2006)
Codenotti, B., Pemmaraju, S., Varadarajan, K.: On the polynomial time computation of equilibria for certain exchange economies. In: SODA 2005 (2005)
Devanur, N.R., Papadimitriou, C.H., Saberi, A., Vazirani, V.V.: Market equilibrium via a primal-dual type algorithm. JACMÂ 55(5) (2008)
Dubey, P., Geanakoplos, J.: From Nash to Walras via Shapley-Shubik. Journal of Mathematical Economics 39, 391–400 (2003)
Edelman, B., Ostrovsky, M., Schwarz, M.: Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords. The American Economic Review 97(1), 242–259 (2007)
Garg, J.: Nash equilibria in Fisher market. Working Manuscript (2010)
Jain, K.: A polynomial time algorithm for computing the Arrow-Debreu market equilibrium for linear utilities. In: FOCS 2004 (2004)
Mas-Colell, A., Whinston, M.D., Green, J.R.: Microeconomic Theory. Oxford University Press, Oxford (1995)
Nash, J.F.: Equilibrium points in n-person games. Proc. of the National Academy of Sciences of the United States of America 36(1), 48–49 (1950)
Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)
Orlin, J.B.: Improved algorithms for computing Fisher’s market clearing prices. In: STOC 2010 (2010)
Samuelson, P.A.: A note on the pure theory of consumers’ behaviour. Economica 5, 61–71 (1938)
Samuelson, P.A.: Foundations of Economic Analysis. Harward University Press (1947)
Shapley, L., Shubik, M.: Trade using one commodity as a means of payment. Journal of Political Economy 85(5), 937–968 (1977)
Varian, H.: Position auctions. International Journal of Industrial Organization 25, 1163–1178 (2007)
Varian, H.: Microeconomic Analysis, 3rd edn (1992)
Walras, L.: Elements of Pure Economics, Translated by Jaffé, Allen & Urwin. London (1954)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Adsul, B., Babu, C.S., Garg, J., Mehta, R., Sohoni, M. (2010). Nash Equilibria in Fisher Market. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds) Algorithmic Game Theory. SAGT 2010. Lecture Notes in Computer Science, vol 6386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16170-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-16170-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16169-8
Online ISBN: 978-3-642-16170-4
eBook Packages: Computer ScienceComputer Science (R0)